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A289971
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Number of permutations of [n] determined by their antidiagonal sums.
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3
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1, 1, 2, 4, 9, 20, 49, 114, 277, 665, 1608, 3875
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OFFSET
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0,3
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LINKS
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MATHEMATICA
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xray[perm_List] := Module[{P, n = Length[perm]}, P[_, _] = 0; Thread[perm -> Range[n]] /. Rule[i_, j_] :> Set[P[i, j], 1]; Table[Sum[P[i - j + 1, j], {j, Max[1, i - n + 1], Min[i, n]}], {i, 1, 2n - 1}]];
a[n_] := xray /@ Permutations[Range[n]] // Tally // Count[#, {_List, 1}]&;
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PROG
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(Sage)
def X_ray(pi):
P = Permutation(pi).to_matrix()
n = P.nrows()
return tuple(sum(P[k-1-j][j] for j in range(max(0, k-n), min(k, n)))
for k in range(1, 2*n))
@cached_function
def X_rays(n):
return sorted(X_ray(pi) for pi in Permutations(n))
def statistic(pi): return X_rays(pi.size()).count(X_ray(pi))
[[statistic(pi) for pi in Permutations(n)].count(1) for n in range(7)]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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